Efficient Probabilistic Subsumption Checking for Content-Based Publish/Subscribe Systems

Abstract

Abstract. Efficient subsumption checking, deciding whether a subscription or publication is covered by a set of previously defined subscriptions, is of paramount importance for publish/subscribe systems. It provides the core system functionality-matching of publications to subscriber needs expressed as subscriptions-and additionally, reduces the overall system load and generated traffic since the covered subscriptions are not propagated in distributed environments. As the subsumption problem was shown previously to be co-NP complete and existing solutions typically apply pairwise comparisons to detect the subsumption relationship, we propose a 'Monte Carlo type' probabilistic algorithm for the general subsumption problem. It determines whether a publication/subscription is covered by a disjunction of subscriptions in O(k m d), where k is the number of subscriptions, m is the number of distinct attributes in subscriptions, and d is the number of tests performed to answer a subsumption question. The probability of error is problem-specific and typically very small, and sets an upper bound on d. Our experimental results show significant gains in term of subscription set reduction which has favorable impact on the overall system performance as it reduces the total computational costs and networking traffic. Furthermore, the expected theoretical bounds underestimate algorithm performance because it performs much better in practice due to introduced optimizations, and is adequate for fast forwarding of subscriptions in case of high subscription rate.

Continuous query evaluation over distributed sensor networks

“…This parameter controls the tradeoff between processing cost and false negatives, i.e., smaller probabilities generate more processing load but less false negatives, and vice versa. We show in [15] that, in practice, the actual error is even smaller and decreases with larger subscription sets. We call this algorithm set filtering, and find it appropriate for distributed data streams, like sensor networks, where data sources could be unreliable, user subscriptions numerous and transmitted data can be lost due to in-network traffic congestion and link failure ( [4], [13]).…”

“…In [15], we propose a probabilistic algorithm, which guarantees detection of set subsumption with a configurable probability of error. The probabilistic aspect can generate false positive decisions that a new subscription is covered by existing ones.…”

Subscription Subsumption Evaluation for Content-Based Publish/Subscribe Systems

“…Ouksel et al present a Monte Carlo type probabilistic algorithm for the subsumption checking [3]. The algorithm has O(k.m.d) time complexity where k is the number of subscriptions, m is the number of distinct attributes (dimensions) in subscriptions, and d is the number of tests performed to detect subsumption of a new subscription.…”

“…The subsumption checking problem where subscriptions can be represented as convex polyhedra has been shown to be co-NP complete [10] 1 . To the best of our knowledge the only work that considers subscription subsumption in pub/sub systems is a 'Monte Carlo type' algorithm for probabilistic subsumption checking proposed by Ouksel et al [3]. However, this technique may falsely determine a subscription to be subsumed by a set of existing subscriptions when in fact it isn't.…”

Content-Based Publish/Subscribe Using Distributed R-Trees

“…However, the merging problem was proved to be NP-hard [9]. An optimization of subscription merging is presented by Ouksel et al [14] where they propose a Monte Carlo type algorithm. Contrary to our approach, the algorithm introduces false negatives due to the probabilistic nature of the algorithm.…”